SET007 Axioms: SET007+560.ax


%------------------------------------------------------------------------------
% File     : SET007+560 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Lawson Topology in Continuous Lattices
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : waybel21 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   73 (   0 unit)
%            Number of atoms       : 1107 (  39 equality)
%            Maximal formula depth :   21 (  12 average)
%            Number of connectives : 1171 ( 137 ~  ;   1  |; 765  &)
%                                         (  15 <=>; 253 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   65 (   0 propositional; 1-4 arity)
%            Number of functors    :   28 (   0 constant; 1-5 arity)
%            Number of variables   :  247 (   0 singleton; 235 !;  12 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_waybel21,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_lattice3(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v19_waybel_0(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_orders_3(C,A,B) ) ) ) ) )).

fof(cc2_waybel21,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_yellow_0(B)
        & v2_lattice3(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( m1_waybel21(C,A,B)
         => ( v1_relat_1(C)
            & v19_waybel_0(C,A,B) ) ) ) )).

fof(rc1_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_yellow_0(B,A)
          & ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v4_orders_2(B)
          & v1_yellow_0(B)
          & v2_yellow_0(B)
          & v3_yellow_0(B)
          & v4_yellow_0(B,A)
          & v5_yellow_0(B,A)
          & v7_yellow_0(B,A)
          & v3_waybel_0(B,A)
          & v4_waybel_0(B,A)
          & v24_waybel_0(B)
          & v25_waybel_0(B)
          & v1_lattice3(B)
          & v2_lattice3(B)
          & v3_lattice3(B) ) ) )).

fof(fc1_waybel21,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k3_yellow_9(A,k1_struct_0(A,B)))
        & v2_orders_2(k3_yellow_9(A,k1_struct_0(A,B)))
        & v3_orders_2(k3_yellow_9(A,k1_struct_0(A,B)))
        & v6_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A)
        & v7_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)))
        & v8_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A)
        & v9_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A)
        & v10_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A)
        & v11_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A) ) ) )).

fof(rc2_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( l1_waybel_0(B,A)
          & ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v6_waybel_0(B,A)
          & v7_waybel_0(B)
          & v8_waybel_0(B,A)
          & v9_waybel_0(B,A)
          & v10_waybel_0(B,A)
          & v11_waybel_0(B,A) ) ) )).

fof(fc2_waybel21,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k3_yellow_9(A,B))
        & v6_waybel_0(k3_yellow_9(A,B),A)
        & v9_waybel_0(k3_yellow_9(A,B),A) ) ) )).

fof(fc3_waybel21,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & v5_orders_3(C,A,B)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & ~ v3_struct_0(D)
        & v9_waybel_0(D,A)
        & l1_waybel_0(D,A) )
     => ( ~ v3_struct_0(k7_waybel_9(A,B,C,D))
        & v6_waybel_0(k7_waybel_9(A,B,C,D),B)
        & v9_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) )).

fof(d1_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ( ( v2_yellow_0(A)
             => v2_yellow_0(B) )
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
               => ( m1_waybel21(C,A,B)
                <=> ! [D] :
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => r3_waybel_0(A,B,C,D) ) ) ) ) ) ) )).

fof(t1_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_yellow_0(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_waybel21(C,A,B)
             => k3_yellow_6(u1_struct_0(A),B,C,k4_yellow_0(A)) = k4_yellow_0(B) ) ) ) )).

fof(t2_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v19_waybel_0(C,A,B)
               => ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & v1_finset_1(D)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => r3_waybel_0(A,B,C,D) ) ) ) ) ) )).

fof(t3_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_yellow_0(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v19_waybel_0(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( k3_yellow_6(u1_struct_0(A),B,C,k4_yellow_0(A)) = k4_yellow_0(B)
               => m1_waybel21(C,A,B) ) ) ) ) )).

fof(t4_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( v19_waybel_0(C,A,B)
                  & ! [D] :
                      ( ( ~ v1_xboole_0(D)
                        & v2_waybel_0(D,A)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => r3_waybel_0(A,B,C,D) ) )
               => ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => r3_waybel_0(A,B,C,D) ) ) ) ) ) )).

fof(t5_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v17_waybel_0(C,A,B)
               => m1_waybel21(C,A,B) ) ) ) ) )).

fof(t6_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_orders_2(D) )
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
                      & g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                              & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                           => ( E = F
                             => ( ( v17_waybel_0(E,A,B)
                                 => v17_waybel_0(F,C,D) )
                                & ( v22_waybel_0(E,A,B)
                                 => v22_waybel_0(F,C,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t7_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_orders_2(D) )
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
                      & g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                              & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                           => ( E = F
                             => ( ( v18_waybel_0(E,A,B)
                                 => v18_waybel_0(F,C,D) )
                                & ( v21_waybel_0(E,A,B)
                                 => v21_waybel_0(F,C,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t8_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => v17_waybel_0(k1_yellow_9(A,B),B,A) ) ) )).

fof(t9_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v8_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => v18_waybel_0(k1_yellow_9(A,B),B,A) ) ) )).

fof(t10_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v4_waybel_0(B,A)
            & m1_yellow_0(B,A) )
         => v22_waybel_0(k1_yellow_9(A,B),B,A) ) ) )).

fof(t11_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v3_waybel_0(B,A)
            & m1_yellow_0(B,A) )
         => v21_waybel_0(k1_yellow_9(A,B),B,A) ) ) )).

fof(t12_waybel21,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( l1_orders_2(C)
             => ! [D] :
                  ( m1_yellow_0(D,A)
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C)) )
                   => ( m1_yellow_0(C,B)
                      & ( v4_yellow_0(D,A)
                       => ( v4_yellow_0(C,B)
                          & m1_yellow_0(C,B) ) ) ) ) ) ) ) ) )).

fof(t13_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v4_yellow_0(A,A)
        & v7_yellow_0(A,A)
        & v8_yellow_0(A,A)
        & m1_yellow_0(A,A) ) ) )).

fof(t14_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( v5_yellow_0(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
               => r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) )).

fof(t15_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( v6_yellow_0(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
               => r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) )).

fof(t16_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v5_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( ( r2_hidden(k4_yellow_0(A),u1_struct_0(B))
              & v3_waybel_0(B,A) )
           => v7_yellow_0(B,A) ) ) ) )).

fof(t17_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v6_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( ( r2_hidden(k3_yellow_0(A),u1_struct_0(B))
              & v4_waybel_0(B,A) )
           => v8_yellow_0(B,A) ) ) ) )).

fof(t18_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( v7_yellow_0(B,A)
           => v3_lattice3(B) ) ) ) )).

fof(t19_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( v8_yellow_0(B,A)
           => v3_lattice3(B) ) ) ) )).

fof(t20_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_yellow_0(D,B)
                    & m1_yellow_0(D,B) )
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & u1_struct_0(C) = u1_struct_0(D)
                      & v7_yellow_0(C,A) )
                   => v7_yellow_0(D,B) ) ) ) ) ) )).

fof(t21_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_yellow_0(D,B)
                    & m1_yellow_0(D,B) )
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & u1_struct_0(C) = u1_struct_0(D)
                      & v8_yellow_0(C,A) )
                   => v8_yellow_0(D,B) ) ) ) ) ) )).

fof(t22_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_yellow_0(D,B)
                    & m1_yellow_0(D,B) )
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & u1_struct_0(C) = u1_struct_0(D)
                      & v4_waybel_0(C,A) )
                   => v4_waybel_0(D,B) ) ) ) ) ) )).

fof(t23_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_yellow_0(D,B)
                    & m1_yellow_0(D,B) )
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & u1_struct_0(C) = u1_struct_0(D)
                      & v3_waybel_0(C,A) )
                   => v3_waybel_0(D,B) ) ) ) ) ) )).

fof(t24_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( v5_pre_topc(D,A,B)
                   => r1_tarski(k4_pre_topc(A,B,D,k11_yellow_6(A,C)),k11_yellow_6(B,k7_waybel_9(A,B,D,C))) ) ) ) ) ) )).

fof(d2_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ( v9_waybel_0(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(B))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ( r1_orders_2(B,C,D)
                     => r1_orders_2(A,k3_waybel_0(A,B,D),k3_waybel_0(A,B,C)) ) ) ) ) ) ) )).

fof(t27_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( r1_tarski(k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)),C)
             => r1_waybel_0(A,B,C) ) ) ) )).

fof(t28_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => k1_waybel11(A,k3_yellow_9(A,B)) = k2_yellow_0(A,B) ) ) )).

fof(t29_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v25_waybel_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v2_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v5_orders_3(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => k1_waybel11(B,k7_waybel_9(A,B,D,k3_yellow_9(A,C))) = k2_yellow_0(B,k4_pre_topc(A,B,D,C)) ) ) ) ) )).

fof(t30_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v2_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v5_orders_3(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v2_waybel_0(E,B)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
                     => ( E = k4_pre_topc(A,B,D,C)
                       => m2_yellow_6(k7_waybel_9(A,B,D,k3_yellow_9(A,C)),B,k3_yellow_9(B,E)) ) ) ) ) ) ) )).

fof(t31_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v2_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v5_orders_3(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v2_waybel_0(E,B)
                        & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
                     => ( E = k4_pre_topc(A,B,D,C)
                       => r1_tarski(k11_yellow_6(B,k3_yellow_9(B,E)),k11_yellow_6(B,k7_waybel_9(A,B,D,k3_yellow_9(A,C)))) ) ) ) ) ) ) )).

fof(t32_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( u1_waybel_0(A,k4_waybel17(A,B)) = k6_relat_1(B)
            & u1_struct_0(k4_waybel17(A,B)) = B
            & v4_yellow_0(k4_waybel17(A,B),A)
            & m1_yellow_0(k4_waybel17(A,B),A) ) ) ) )).

fof(t33_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_orders_3(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_waybel_0(D,A)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => k1_waybel11(B,k7_waybel_9(A,B,C,k4_waybel17(A,D))) = k1_yellow_0(B,k4_pre_topc(A,B,C,D)) ) ) ) ) )).

fof(t34_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k4_waybel17(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k4_waybel17(A,B)))
                 => ( r3_orders_2(k4_waybel17(A,B),C,D)
                  <=> r3_orders_2(A,k3_waybel_0(A,k4_waybel17(A,B),C),k3_waybel_0(A,k4_waybel17(A,B),D)) ) ) ) ) ) )).

fof(t35_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r2_hidden(k1_yellow_0(A,B),k11_yellow_6(A,k4_waybel17(A,B))) ) ) )).

fof(d3_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_waybel_0(C,A) )
             => ( m2_yellow_6(C,A,B)
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
                      & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
                   => ( m2_waybel21(D,A,B,C)
                    <=> ( u1_waybel_0(A,C) = k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,u1_waybel_0(A,B))
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                           => ? [F] :
                                ( m1_subset_1(F,u1_struct_0(C))
                                & ! [G] :
                                    ( m1_subset_1(G,u1_struct_0(C))
                                   => ( r1_orders_2(C,F,G)
                                     => r1_orders_2(B,E,k3_yellow_6(u1_struct_0(C),B,D,G)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m2_yellow_6(C,A,B) )
             => ! [D] :
                  ( m2_waybel21(D,A,B,C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => k3_waybel_0(A,C,E) = k3_waybel_0(A,B,k3_yellow_6(u1_struct_0(C),B,D,E)) ) ) ) ) ) )).

fof(t37_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m2_yellow_6(C,A,B)
             => r3_orders_2(A,k1_waybel11(A,B),k1_waybel11(A,C)) ) ) ) )).

fof(t38_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m2_yellow_6(C,A,B)
             => ! [D] :
                  ( m2_waybel21(D,A,B,C)
                 => ( ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(C))
                           => ~ ( r1_orders_2(B,k3_yellow_6(u1_struct_0(C),B,D,F),E)
                                & ! [G] :
                                    ( m1_subset_1(G,u1_struct_0(C))
                                   => ~ ( r1_orders_2(C,F,G)
                                        & r1_orders_2(A,k3_waybel_0(A,C,G),k3_waybel_0(A,B,E)) ) ) ) ) )
                   => k1_waybel11(A,B) = k1_waybel11(A,C) ) ) ) ) ) )).

fof(t39_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_yellow_6(C,A,B)
                & m1_yellow_6(C,A,B) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ? [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                        & r1_orders_2(B,D,E)
                        & r2_hidden(E,u1_struct_0(C)) ) )
               => ( m2_yellow_6(C,A,B)
                  & m2_waybel21(k1_yellow_9(B,C),A,B,C) ) ) ) ) ) )).

fof(t40_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ( m2_yellow_6(k6_waybel_9(A,B,C),A,B)
                & m2_waybel21(k1_yellow_9(B,k6_waybel_9(A,B,C)),A,B,k6_waybel_9(A,B,C)) ) ) ) ) )).

fof(t41_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k1_waybel11(A,k6_waybel_9(A,B,C)) = k1_waybel11(A,B) ) ) ) )).

fof(t42_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ~ ( r1_waybel_0(A,B,C)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ~ ( r2_hidden(k3_waybel_0(A,B,D),C)
                        & r1_tarski(k8_yellow_2(u1_struct_0(k6_waybel_9(A,B,D)),A,u1_waybel_0(A,k6_waybel_9(A,B,D))),C) ) ) ) ) ) )).

fof(t43_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v11_waybel_0(B,A)
            & l1_waybel_0(B,A) )
         => ( ~ v1_xboole_0(k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)))
            & v2_waybel_0(k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)),A)
            & m1_subset_1(k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t44_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v11_waybel_0(B,A)
            & l1_waybel_0(B,A) )
         => k11_yellow_6(A,B) = k1_struct_0(A,k2_waybel_9(A,B)) ) ) )).

fof(t45_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v2_waybel19(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v19_waybel_0(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v5_pre_topc(C,A,B)
              <=> ( v22_waybel_0(C,A,B)
                  & ! [D] :
                      ( ( ~ v1_xboole_0(D)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => r3_waybel_0(A,B,C,D) ) ) ) ) ) ) )).

fof(t46_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v2_waybel19(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( m1_waybel21(C,A,B)
             => ( v5_pre_topc(C,A,B)
              <=> ( v17_waybel_0(C,A,B)
                  & v22_waybel_0(C,A,B) ) ) ) ) ) )).

fof(d4_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_waybel21(C,A,B)
              <=> ! [D] :
                    ( ( ~ v3_struct_0(D)
                      & v3_orders_2(D)
                      & v7_waybel_0(D)
                      & l1_waybel_0(D,A) )
                   => k3_yellow_6(u1_struct_0(A),B,C,k1_waybel11(A,D)) = k1_waybel11(B,k7_waybel_9(A,B,C,D)) ) ) ) ) ) )).

fof(t47_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v2_waybel19(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( m1_waybel21(C,A,B)
             => ( v5_pre_topc(C,A,B)
              <=> v1_waybel21(C,A,B) ) ) ) ) )).

fof(t48_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v5_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( r2_hidden(k4_yellow_0(A),u1_struct_0(B))
           => ( ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( C = u1_struct_0(B)
                      & v4_pre_topc(C,A) ) )
              | v7_yellow_0(B,A) ) ) ) ) )).

fof(t49_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( ? [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & C = u1_struct_0(B)
                & v4_pre_topc(C,A) )
           => v4_waybel_0(B,A) ) ) ) )).

fof(t50_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & v4_waybel_0(B,A)
            & m1_yellow_0(B,A) )
         => ? [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
              & C = u1_struct_0(B)
              & v4_pre_topc(C,A) ) ) ) )).

fof(t51_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & v4_waybel_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ( r1_waybel_0(A,C,u1_struct_0(B))
               => r2_hidden(k1_waybel11(A,C),u1_struct_0(B)) ) ) ) ) )).

fof(t52_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v5_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( ( r2_hidden(k4_yellow_0(A),u1_struct_0(B))
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v3_orders_2(C)
                    & v7_waybel_0(C)
                    & l1_waybel_0(C,A) )
                 => ( r1_tarski(k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C)),u1_struct_0(B))
                   => r2_hidden(k1_waybel11(A,C),u1_struct_0(B)) ) ) )
           => v7_yellow_0(B,A) ) ) ) )).

fof(t53_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_orders_2(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( r1_tarski(k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C)),u1_struct_0(B))
                 => r2_hidden(k1_waybel11(A,C),u1_struct_0(B)) ) )
           => v4_waybel_0(B,A) ) ) ) )).

fof(t54_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v5_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( C = u1_struct_0(B)
                  & r2_hidden(k4_yellow_0(A),C) )
               => ( v4_pre_topc(C,A)
                <=> ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & v3_orders_2(D)
                        & v7_waybel_0(D)
                        & l1_waybel_0(D,A) )
                     => ( r1_waybel_0(A,D,C)
                       => r2_hidden(k1_waybel11(A,D),C) ) ) ) ) ) ) ) )).

fof(dt_m1_waybel21,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_lattice3(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( m1_waybel21(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
            & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) )).

fof(existence_m1_waybel21,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_lattice3(B)
        & l1_orders_2(B) )
     => ? [C] : m1_waybel21(C,A,B) ) )).

fof(dt_m2_waybel21,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & ~ v3_struct_0(C)
        & l1_waybel_0(C,A) )
     => ! [D] :
          ( m2_waybel21(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
            & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) ) ) ) )).

fof(existence_m2_waybel21,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & ~ v3_struct_0(C)
        & l1_waybel_0(C,A) )
     => ? [D] : m2_waybel21(D,A,B,C) ) )).

fof(t25_waybel21,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ( ~ v1_xboole_0(a_2_0_waybel21(A,B))
            & v1_waybel_0(a_2_0_waybel21(A,B),A)
            & m1_subset_1(a_2_0_waybel21(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t26_waybel21,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v8_waybel_0(B,A)
            & l1_waybel_0(B,A) )
         => ( ~ v1_xboole_0(a_2_1_waybel21(A,B))
            & v1_waybel_0(a_2_1_waybel21(A,B),A)
            & m1_subset_1(a_2_1_waybel21(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(fraenkel_a_2_0_waybel21,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B) )
     => ( r2_hidden(A,a_2_0_waybel21(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k2_yellow_0(B,a_3_0_waybel21(B,C,D)) ) ) ) )).

fof(fraenkel_a_3_0_waybel21,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_0_waybel21(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_waybel_0(B,C,E)
            & r1_orders_2(C,D,E) ) ) ) )).

fof(fraenkel_a_2_1_waybel21,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v2_orders_2(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & v8_waybel_0(C,B)
        & l1_waybel_0(C,B) )
     => ( r2_hidden(A,a_2_1_waybel21(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k2_yellow_0(B,a_3_1_waybel21(B,C,D)) ) ) ) )).

fof(fraenkel_a_3_1_waybel21,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v2_orders_2(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & v8_waybel_0(C,B)
        & l1_waybel_0(C,B)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_1_waybel21(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_waybel_0(B,C,E)
            & r1_orders_2(C,D,E) ) ) ) )).
%------------------------------------------------------------------------------